However, with LBC they've recently instated new rules in terms of KYC for users with significant volumes. Similar stuff with hodlhodl and bisq, just that there is a lot less offers.
I don't know what you are talking about with Bisq. There is no KYC nor anything similar and there never was.
It is completely a P2P exchange, it is permission-less and you don't need to register at any site nor anywhere centralized to start making and taking offers.
It uses simple multisig transactions on a Bitcoin network and Tor for it's P2P network. No blockchain, no website, no company.
Just code to let users find each other and safely trade using multisig deposits. Very simple, very private and very secure.
You can trade without any verification whatsoever and you always could.